Mathematical Sciences: Problems in Function Theory and Operator Theory

本研究涉及算子理论与函数理论交界处的几个问题。该项目的第一部分涉及多项式逼近，旨在了解闭单位圆盘上的某些度量。该项目的另一部分涉及对不同解析函数空间上的复合算子的研究。这包括确定复合算子的谱的工作，继续研究大型加权Bergman空间上的复合算子的工作，以及确定一致算子拓扑中复合算子空间中的分支的问题。这项研究属于现代分析的一般领域，如上所述，处于算子理论和函数理论的交界处。这项研究涉及到一个或多个复变量的解析函数空间上的复合算子的研究，是现代复变分析理论的一个中心课题。

This research concerns several problems which lie at the interface of operator theory and function theory. The first part of the project involves polynomial approximation directed at understanding certain measures on the closed unit disc. The other part of the project involves a study of the composition operators on various spaces of analytic functions. This includes work on identifying the spectrum of a composition operator, continuing work on the study of composition operators on large weighted Bergman spaces, and the question of identifying the components in the space of composition operators in the uniform operator topology. This research is in the general area of modern analysis and, as noted above, lies at the interface of operator theory and function theory. The research involves the study of composition operators on spaces of analytic functions in one or several complex variables and is a central topic in the modern theory of complex analysis.